Thursday, February 27, 2014

The Full Adder Circuit

I recently wrote a very brief introduction to Boolean algebra for the glossary, so I thought it would be worth describing a very simple but important application example. There are two main reasons why I'm interested in Boolean algebra. The first is that in probability theory, the hypotheses we investigate are assumed to be Boolean in character (true or false, with no intermediates allowed). The second is that Boolean algebra is an important branch of logic, and therefore intimately linked to science and rationality.

In an earlier post, I discussed how all transfer of information comes down to a sequence of answers to yes/no questions. In this spirit, therefore, consider the following:
By answering only yes/no type questions, calculate the sum 234 + 111. In other words, if you were a digital computer, how would you perform this calculation?

Sunday, February 2, 2014

Practical Morality, Part 2

It has been said that democracy is the worst form of government, except all those others that have been tried.
Winston Churchill 

(The second of two parts. Read the first installment here.)

Politics & Science

I have a funny little feeling that Churchill actually knew a small bit about politics. According to dear, old Winston, democracy sucks. But why does it suck? And does it necessarily suck?

A full analysis of these questions could run into thousands of pages, and obviously stretches far beyond any area in which I could claim expertise, but for now at least, I want to point out just one aspect of democracy's poor performance to date that can most definitely be fixed. That is, the failure so far of both politicians and the electorate to explicitly recognize the necessarily rational basis for morality.